XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-17-ext
Number of variables: 51
Number of constraints: 1275
Satisfiable: True
Timestamp: 2025-07-27 21:34:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 51
Number of constraints: 1275

General features

Coarse blocks: 129,370
Value tables: 51

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 2,550 MAX VALUE 883.76 0.00 0.00 0.00

Coarse blocks size 1 50 48.94 50.00 6,331,890 MAX VALUE 495,192.00 7.12 0.15 0.10

Relational linkage 0.02 0.02 0.02 0.02 37.67 0.00 -7,553.04 0.00 0.00 0.00

Tightness 0.02 0.99 0.05 0.02 57.80 0.00 -4,879.94 0.16 3.43 0.20

Tuples 33 2,550 2,483.09 2,550.00 3,165,940 MAX VALUE 9,860.23 404.22 0.16 0.20

Values 51 51 51.00 51.00 2,601 MAX VALUE 200.52 0.00 0.00 0.00

Value table constraints 50 50 50.00 50.00 2,550 MAX VALUE 199.51 0.00 0.00 0.00

Value table partitions 51 51 51.00 51.00 2,601 MAX VALUE 200.52 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	2,550	MAX VALUE	883.76	0.00	0.00	0.00
Coarse blocks size	1	50	48.94	50.00	6,331,890	MAX VALUE	495,192.00	7.12	0.15	0.10
Relational linkage	0.02	0.02	0.02	0.02	37.67	0.00	-7,553.04	0.00	0.00	0.00
Tightness	0.02	0.99	0.05	0.02	57.80	0.00	-4,879.94	0.16	3.43	0.20
Tuples	33	2,550	2,483.09	2,550.00	3,165,940	MAX VALUE	9,860.23	404.22	0.16	0.20
Values	51	51	51.00	51.00	2,601	MAX VALUE	200.52	0.00	0.00	0.00
Value table constraints	50	50	50.00	50.00	2,550	MAX VALUE	199.51	0.00	0.00	0.00
Value table partitions	51	51	51.00	51.00	2,601	MAX VALUE	200.52	0.00	0.00	0.00

Tree decomposition

Number of clusters: 1
Number of leaves: 1
Tree depth: 0
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 1,275 1,275 1,275.00 1,275.00 1,275 1,275 7.15 0.00 0.00 0.00

Variables per cluster 51 51 51.00 51.00 51 51 3.93 0.00 0.00 0.00

Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Separator variables 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Clusters per var 1 1 1.00 1.00 51 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	1,275	1,275	1,275.00	1,275.00	1,275	1,275	7.15	0.00
Variables per cluster	51	51	51.00	51.00	51	51	3.93	0.00
Separator constraints	0	0	0.00	0.00	0	0	None	None
Separator variables	0	0	0.00	0.00	0	0	None	None
Clusters per var	1	1	1.00	1.00	51	1	0.00	0.00

Dual tree decomposition

Number of clusters: 49
Number of leaves: 25
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 2,499 26,524 5,818.00 2,499.00 285,082 MAX VALUE 410.46 5,582.02 0.96 1.45

Variables per cluster 99 824 211.45 99.00 10,361 MAX VALUE 250.54 177.70 0.84 1.45

Separator constraints 0 15,876 4,543.00 2,401.00 222,607 0 None 3,370.57 0.74 1.45

Separator variables 0 648 185.43 98.00 9,086 0 None 137.57 0.74 1.45

Clusters per variable 1 10 8.13 9.00 10,361 MAX VALUE 2,599.45 2.05 0.25 1.75

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2,499	26,524	5,818.00	2,499.00	285,082	MAX VALUE	410.46	5,582.02	0.96	1.45
Variables per cluster	99	824	211.45	99.00	10,361	MAX VALUE	250.54	177.70	0.84	1.45
Separator constraints	0	15,876	4,543.00	2,401.00	222,607	0	None	3,370.57	0.74	1.45
Separator variables	0	648	185.43	98.00	9,086	0	None	137.57	0.74	1.45
Clusters per variable	1	10	8.13	9.00	10,361	MAX VALUE	2,599.45	2.05	0.25	1.75

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 20,825
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 1.00 1.00 1.00 1.00 51.00 1.00 0.00 0.00 0.00 0.00

Degree 50 50 50.00 50.00 2,550 MAX VALUE 199.51 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 51 1 0.00 0.00 0.00 0.00

MCB cycle size None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	51.00	1.00	0.00	0.00	0.00	0.00
Degree	50	50	50.00	50.00	2,550	MAX VALUE	199.51	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	51	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 20,825

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 1.00 1.00 1.00 1.00 51.00 1.00 0.00 0.00 0.00 0.00

Degree 50 50 50.00 50.00 2,550 MAX VALUE 199.51 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 51 1 0.00 0.00 0.00 0.00

MCB cycle size None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	51.00	1.00	0.00	0.00	0.00	0.00
Degree	50	50	50.00	50.00	2,550	MAX VALUE	199.51	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	51	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 7.69%
MCB compute time (ms): 287,150
MCB cycles: 61,201
Triangles: 1,020,420
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.51 0.51 0.51 0.51 644.07 0.00 -870.69 0.00 0.00 0.00

Degree 98 98 98.00 98.00 124,950 MAX VALUE 5,845.83 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 2,550 MAX VALUE 883.76 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 183,603 MAX VALUE 67,236.20 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)
Clustering coefficient	0.51	0.51	0.51	0.51	644.07	0.00	-870.69
Degree	98	98	98.00	98.00	124,950	MAX VALUE	5,845.83
Eccentricity	2	2	2.00	2.00	2,550	MAX VALUE	883.76
MCB cycle size	3	3	3.00	3.00	183,603	MAX VALUE	67,236.20

Minimal dual graph

Density: 0.31%
MCB compute time (ms): 78,529
MCB cycles: 1,231

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.01 21.40 0.02

Degree 2 7 3.92 4.00 4,998 MAX VALUE 1,704.51 0.98 0.25 1.27

Eccentricity 11 19 14.54 14.00 18,535 MAX VALUE 3,405.21 1.59 0.11 1.86

MCB cycle size 3 17 6.03 6.00 7,429 MAX VALUE 2,185.76 1.23 0.20 1.36

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.01	21.40	0.02
Degree	2	7	3.92	4.00	4,998	MAX VALUE	1,704.51	0.98	0.25	1.27
Eccentricity	11	19	14.54	14.00	18,535	MAX VALUE	3,405.21	1.59	0.11	1.86
MCB cycle size	3	17	6.03	6.00	7,429	MAX VALUE	2,185.76	1.23	0.20	1.36

Triangulated dual graph

Density: None%
Triangles: None

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 5.35%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.47 1.00 0.82 0.79 1,042.18 0.00 -278.69 0.15 0.18 4.27

Degree 2 325 68.20 9.00 86,950 MAX VALUE 3,646.27 102.94 1.51 3.91

Eccentricity 3 6 4.54 5.00 5,784 MAX VALUE 1,916.80 0.59 0.13 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.79	1,042.18	0.00	-278.69	0.15	0.18	4.27
Degree	2	325	68.20	9.00	86,950	MAX VALUE	3,646.27	102.94	1.51	3.91
Eccentricity	3	6	4.54	5.00	5,784	MAX VALUE	1,916.80	0.59	0.13	0.89

Incidence graph

Density: 0.29%
MCB compute time (ms): 5,336
MCB cycles: 1,225
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-17-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 50 3.85 2.00 5,100 MAX VALUE 1,083.28 9.23 2.40 0.16

Eccentricity 3 4 3.96 4.00 5,253 MAX VALUE 1,823.55 0.19 0.05 0.16

MCB cycle size 6 6 6.00 6.00 7,350 MAX VALUE 2,194.91 0.00 0.00 0.00

XCSP 2.1 Benchmarks